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Atlanta (CNN)As protests against police brutality continue across the country, signs of cooperation between demonstrators and law enforcement emerged in Atlanta.

After meeting with four protest leaders for 45 minutes late Monday into early Tuesday, Atlanta Mayor Kasim Reed and Police Chief George Turner agreed to sit down with the protesters for two hours on Monday.

"Tonight was about listening and being open. It was very important that we respect the energy that they were putting into this," Reed told reporters after the meeting. "We're the city of Atlanta -- we're the home of the Civil Rights movement in America."

Monday marked the fifth day in a row of protests in the city. Many are angry after two black men were shot to death by police. After those shootings, five police officers in Dallas were killed by a gunman who said he was targeting white cops.

Demonstrators began their march blocking traffic near the upscale Lenox Square mall in they city's Buckhead neighborhood and continued onto the governor's mansion, where they were met by Reed and Turner.

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"They wanted to have a conversation with us and that's what we're out here to do -- have a conversation," Turner told reporters. "Our city is doing the right things -- that's why we're out here. We're out here trying to have a conversation with folks and figure out what we can do to move our police department to a better place."

Memphis meeting follows weekend of unrest

Black Lives Matter held its first official march in ChicagoMonday evening.

In Memphis, Tennessee, Mayor Jim Strickland and police officials held a town-hall meeting with local movement leaders and the public at which people were able to vent frustrations on a variety of issues, including the need for community policing, better diversity training for police, equal protection for all citizens and sustained funding for youth and crime-prevention programs.

"Our babies our dying because their basketball goals are falling apart," said Rev. DeVante Hill, who was on the panel with the mayor. "There are more empty building in this city than there are playgrounds."

Strickland resisted pressure from the crowd and panel to announce that interim Police Department Director Mike Rallings would get the job permanently, saying only he had been a longtime admirer of his abilities.

"I've been impressed with Mike Rallings for years," Strickland said during the raucous meeting. "I've asked him to apply for the job and I think last night we saw why I asked him to do that."

Arrests

Over the weekend, authorities, protest leaders and the mother of one of the victims have appealed for calm as over 300 demonstrators, angry at the latest killings of black men by police officers, were arrested in a weekend of intense, sometimes violent nationwide protests.

Late Sunday and into Monday morning, almost 50 protesters were bundled into the back of police vans in Baton Rouge, Louisiana. A handful in Atlanta were also arrested.

Then Strickland said he remained "hopeful" that his city's peaceful protests Sunday would signal a willingness of Black Lives Matter activists and police to hold a "respectful" dialog.

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"We are here to fully support those conversations -- and my door has always been open," Strickland said Sunday night in a statement after Interstate 40 for had been closed for a few hours by protestors.

"But we want to do it in a legal way, as well. Let me be clear: you can exercise your First Amendment rights without breaking the law."

Valerie Castile, mother of Philando Castile, one of two black men killed by police last week in separate shootings, sent a statement to media via her attorney Sunday.

"We urge all people to remain peaceful in all demonstrations throughout our community and our nation," the statement read.

"When demonstrations become violent, it disrespects my son and his memory. Philando was a man of peace and dignity.

"I ask you to at all times remain peaceful in your expressions of concern regarding his death at the hands of the police. I promise that we will not rest until justice prevails."

In Boston, organizers for Sunday's demonstration announced on Facebook: "This is a peaceful protest. Please keep violence at home."

Despite the calls for calm from all sides, at least 312 people have been arrested over the weekend at protests from New York to Chicago, and in St. Paul, Minnesota, and Baton Rouge, Louisiana, where two black men, Philando Castile and Alton Sterling, were shot to death by police.

The two men's deaths in turn spurred a lone shooter in Dallas to kill five police officers during a Black Lives Matter protest.

Prominent activist arrested

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Black Lives Matter activist DeRay Mckesson, a public school administrator who is considered among the movement's loudest voices, was among 125 people arrested Saturday night in Baton Rouge, where Alton Sterling was shot and killed last week.

In St. Paul, about102 protesters were arrested. They were demonstrating against the killing of Philando Castile, a school nutrition services supervisor. Last week, Castile was driving a car and was with his girlfriend, Diamond Reynolds, when they were pulled over for a broken taillight.

Reynolds posted a Facebook video of the aftermath of Castile's shooting. Castile told the officer he was armed and had a concealed carry permit, she said. The officer asked him for his license and registration and as he went to retrieve those items, the officer shot him multiple times, she explains as the recording continues.

Baton Rouge Police Chief Carl Dabadie Jr., at a press conference Sunday to explain the arrests, acknowledged a Baton Rouge officer pointed an assault weapon at protesters, but he said a supervisor immediately intervened to secure the weapon from her.

"That is being addressed by us also," Dabadie said. "My officers are human. They are tired. They are scared."

Louisiana Gov. John Bel Edwards, who called the press conference, said most protests had been peaceful -- with most arrests for minor offenses -- and blamed outside agitators for incitements to violence.

"That will not be tolerated -- we don't operate like that in Louisiana," Edwards said. "The best way to honor the memory of Alton Sterling, the Dallas officers and Philando Castile, is through peaceful protest.

"It is critically important that you follow the directions of law enforcement."

Sunday protests

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More marches took place around the nation Sunday.

In Washington, on the fourth night of protests, several hundred protesters who had marched two miles to Union Station accepted without complaint the news from organizers and police that they could not march on the Capitol without a permit.

At the rally, the Rev. Matthew Watley, of Reid Temple AME Church, said people are looking for healing after having old wounds of racism reopened by the events last week.

He also said he wants the community to work with law enforcement.

"We don't want to be profiled as African-Americans, we also can't profile law enforcement because the supermajority of them are trying to do the right thing," he said.